Prior to the present invention casinos have been confronted with a major and costly problem in the game of black-jack, of losing considerable amounts of money to persons known as card-counters who keep a mathematical account of which cards have been thus-far played and the mathematical probabilities of for example beating the dealer by obtaining five cards totaling less than value 21, or by obtaining a card combination close to 21 but not exceeding it, or by obtaining a card combination known as "black-jack". Whenever a card-counter is present, other players are quick to become aware of him and follow his betting and playing tactics to thereby also increase significantly their winnings at the great expense of the "house" represented by the dealer. To partially counter such major advantage achievable by card counters, the dealers have resorted to playing with a combination of several decks up to about eight decks shuffled-together, for a single game or partial-game of dealings for the game of black-jack, to thereby decrease the ability of the card-counter to rapidly arrive at any major advantage during earlier phases of a black-jack game. However, other considerations have also prompted and led to the present invention, such as the inventors' recognition that in order for the card-counters to effectively operate--particularly as multiple decks are employed, sufficient time for accounting and mathematical computations is necessary such as the time between consecutive dealings. But of even greater importance, the inventors observed that between consecutive shufflings of cards there is a time interval of about eleven minutes, of which the card-shuffling consumes about three minutes possibly--which amounts to as much as 27 percent of total playing time, or conservatively at least 20 percent loss of potential earning as compared to no loss of time during the shuffling procedure, such loss amounting to about ten to fifteen million dollars per year, particularly when taken with losses incurred as a result of the card-counters. By eliminating these down-times and making easier the job of the dealer, considerable savings as against losses to card-counters, and improved profits from increased playing time could be achieved. Also, by a novel shuffling machine obtaining improved random mixing of cards and more quickly obtained, predictability by card-counters of probabilities is substantially decreased.